This article is cited in 2 papers

The Simplest Tauberian Theorem

A. F. Grishin

V. N. Karazin Kharkiv National University

Abstract: The following problem is considered: obtain the asymptotic properties of a function $u$ from the asymptotic properties of the integral $\int_0^r{u(t)}dt$. As is well known, this can be done under additional constraints on the function $u(t)$. In this paper, we obtain a theorem in which these constraints are weaker than in other well-known versions of such theorems.

UDC: 517

Received: 19.02.2001
Revised: 25.07.2002

DOI: 10.4213/mzm258

 English version: Mathematical Notes, 2003, 74:2, 212–219

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